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Question

Verify the given linear approximation at a=0. Then use a graphing calculator or computer to determine the values of x for which the linear approximation is accurate to within 0.05. (Round your answer to two decimal places. Enter your answer using interval notation.)

tanx≈x

Answer 1

Use L(x)= f(a)+f'(a)(x-a)

Where f(x) = tan(x)

f'(x) = sec²(x)

L(x) = tan(a)+sec²(x)(x-a)

At a = 0

L(x) = 0 + (1)(x-0) = x

tan(x) ≈ L(x) = x

If you graph f(x) = tan(x) and g(x) = x, pick off all the intersections of f(x) and g(x).